Question

Let the graph of g be a horizontal shrink by a factor of 1/3, followed by a translation 1 unit up of the graph of f(x) = x2. Write a rule for g.

Answer 1

Explanation:

To find the rule for g, we first apply the horizontal shrink by a factor of 1/3 to f(x) = x^2. This shrink is achieved by replacing x with 3x in the function. So, the first transformation gives us:

g₁(x) = f(3x) = (3x)^2 = 9x^2.

Next, we translate g₁ 1 unit up. This is achieved by adding 1 to the function. So, the final rule for g is:

g(x) = g₁(x) + 1 = 9x^2 + 1